Portrait of Adam Weishaupt from 1748
Adam Weishaupt was the son of George Weishaupt, who was a rabbi in Ingolstadt (Bavaria). After his father’s death, when he was 5 years old, Weishaupt came under the tutelage of Johann Adam Freiherr von Ickstatt, both his grandfather and godfather, and who changed his name from Weisthaupt to Ickstatt after he abandoned the Jewish faith. Ickstatt was a professor of law at the University of Ingolstadt, and initiated Weishaupt in rationalism and the philosophies of the enlightenment. Weishaupt was educated in a Jesuit school (order which he later despised). He also studied law, economy, politics, history and various occult philosophies. In 1771 Weishaupt met a Danish trader named Franz Kolmer, who initiated him into Egyptian magical practices and the doctrines of antireligious Manichaeism; after which he developed an anarchist spirit. In 1772 Weisthaupt became a professor in law, and then a professor in cannon law in 1773 after Pope Clement XIV suppressed the Jesuit order.
Weishaupt travelled through France between 1773 and 1775; were he made a friendship with the Marquis de Lafayette (general in the American Revolution and personal friend to Washington and Franklin, promoter of the French Revolution, member of the National Assembly, general of the revolutionary army, commander of the National Guard in Paris,  and Freemason ) and with Maximilien Robespierre (one of the most influential figures of the French Revolution, and a central figure in the Jacobin Club ).
Weishaupt was initiated into Freemasonry in the Lodge "Theodor zum guten Rath (Theodore of Good Council)" in Munich in 1777.  However, soon after, he became disappointed with Freemasonry; as he considered it a simple social club. He decided to found his own order in 1776, based on what he learned in the Jesuits and the Freemasons. The order was first called “Order of Perfectibilists” and later “the Bavarian Illuminati”. He adopted the code name “Spartacus”, as he considered himself a liberator of the human consciousness and of the dogmas and religions that enslaved men. The mission of the order was the abolition of all monarchical governments and state religions in Europe and its colonies.
Due to the small number of members the order had, Weishaupt asked one of his adepts, Baron Adolph von Knigge, for help. The Baron was a German freemason, born near Hanover in 1752;  where Mayer Rothschild worked for the Oppenheimer family. Thanks to the reputation acquired through his work with the Oppenheimer banking house and William I, Mayer Rothschild had frequent deals and contacts with Royals and Nobles; but a direct connection between Mayer and the Baron cannot be confirmed. However, it is confirmed that the Baron funded and gave a great impulse to the Illuminati order; which helped in the recruitment of adepts and the creation of many lodges throughout Germany, France, Austria, Italy, Switzerland and Russia. The order formed an elaborate network of spies and counter-spies throughout Europe. The structure of the order consited in isolated cells of initiates, which reported to a superior whom they did not know; a party structure that would be effectively adopted by some later groups.
In 1777, the Illuminati began to cooperate with all Masonic lodges in order to infiltrate them (especially the Grand Orient of France, of which Franklin was a member). When Weishaupt himself became a member of the Grand Orient, the lodge was backed financially by Mayer Amschel Rothschild to conspire against the establishment.  The Duke of Brunswick himself (Grand Master of Germany) said in 1794 that the Masonic lodges were controlled by the Illuminati. Also Winston Churchill was convinced this was the case, and in 1920 wrote: "This conspiracy against civilization dates from the days of Weishaupt ... as a modern historian Mrs. Webster has so ably shown, it played a recognizable role on the French Revolution."  It is also believed that Weishaupt formed an inner council of members (the “law of five”), which included: himself, Sir Francis Dashwood (Hellfire Club), Kolmer, Alphonse Donatien De Sade (Marquis de Sade) and Mayer Amschel Rothschild. [*]
The order was operative across Europe until 1784, when a messenger en route from Frankfurt am Main (where the Rothschild's shop was located) to Paris was struck by a lightning. On the dead body, the authorities discovered a piece of paper written by Weishaupt himself, and titled "The Original Shift in Days of Illumination". The content described the future goal for "the New World Order through Revolution" and notes for the French revolution (which began just 4 years later); the destiny of these writings was the Grand Orient of France. [*] Soon after, on the 22 of June 1784, the Bavarian authorities also discovered more documents in Weishaupt’s home on how to control all facets of Freemasonry, overthrown all European Monarchies and put an end to the Catholic Church using the same methods that the Jesuits used to protect it from Protestantism. The authorities ordered the prosecution of all members of Freemasonry and the Illuminati. However, Weishaupt and his family escaped with the helped of Ernest II, Duke of Saxe-Gotha-Altenburg (also a Freemason and member of the Illuminati ). He lived in Gotha under the Duke's protection until his death on the 18th of November 1830; still renouncing from the Catholic faith.
… Next Chapter: The Illuminati in America
Wikipedia: Adam Weishaupt (http://en.wikipedia.org/wiki/Adam_Weishaupt) and (http://es.wikipedia.org/wiki/Adam_Weishaupt)
 Wikipedia: Marqués de La Fayette (http://es.wikipedia.org/wiki/Marqu%C3%A9s_de_La_Fayette)
 The Colonial Williamsburg Foundation (http://www.history.org/Almanack/peop...olafayette.cfm)
 Wikipedia: Maximilien Robespierre (http://en.wikipedia.org/wiki/Maximilien_Robespierre)
 Henry Coston, “La Conjuration des Illuminés”, pp. xxxvii-xxxviii. Pb. 304 pp., Paris, 1979.
 Henry Wilson Coil, “Coil's Masonic Encyclopedia”, 1961
 Nesta Helen Webster, “The French Revolution: a Study in Democracy”, London, Constable & Co., 1919
 Wikipedia: Nesta Helen Webster (http://en.wikipedia.org/wiki/Nesta_Helen_Webster)
 William Schnoebelen, “Masonry: Beyond the Light”, Ontario, 1991
 Kris Millegan, “Everything You Ever Wanted to Know About Skull and Bones But Were Afraid to Ask”, 1996.
 Wikipedia: Ernest II, Duke of Saxe-Gotha-Altenburg (http://en.wikipedia.org/wiki/Ernest_...otha-Altenburg)
[*] I couldn't find better sources for these two statement.